Super resolving partial wave analyzer-transceiver

Abstract

Methods and electronic apparatus for recovering relatively high-resolution information from a partial wave representation of an information signal. According to the invention, there is provided a method of operating on a given partial wave function, or of producing a partial wave representation of an information signal as part of the method. Portions of the partial wave representation of the information signal are synchronously selected as by signal sampling under control of an interpolated high frequency clock. An inverse partial wave representation of the selected portions of the transformed signal is then performed, and the inverse partial wave representation is linearly deconvolved to produce a high resolution equivalent of high-resolution information signal. The invention may include an analytic converter for removing the effects of any dispersion of the partial wave representation. While the concepts involved are universally adaptable to signal processing systems, preferred embodiments of the invention as applied to a modem network and to an interferometer are described.

I claim: 
     
       1. In a signal processing system having a system input, a signal transmission channel, and a system output, an improved apparatus for receiving a high resolution signal at the system input and recovering a corresponding high-resolution information signal at the system output, said apparatus comprising: means for producing a summation of wave functions representing said input signal;   means for truncating said summation of wave functions to produce a corresponding summation of partial wave functions;   means for transmitting the truncated summation of partial wave functions through the signal transmission channel;   means for detecting the transmitted truncated summation of partial wave functions;   means responsive to said detecting means for producing a partial wave spectrum from the detected summation of partial wave functions; and   means for deconvolving said partial-wave spectrum to the values of said system input signal.   
     
     
       2. The apparatus as claimed in claim 1, wherein; said truncated summation of partial wave functions comprises real and imaginary parts; and   only said real part is transmitted through the signal transmission channel of said system.   
     
     
       3. The apparatus as claimed in claim 1, wherein said summation of wave functions representing said input signal exists over a first interval, and said truncated summation of partial wave functions exists over a second interval, said second interval being M times shorter than said first interval, where M is the data compression ratio of the system. 
     
     
       4. The apparatus as claimed in claim 2, wherein said real part of said transmitted signal has even and odd components, and wherein said detecting means comprises: means for detecting and outputting said even component;   means for detecting and outputting said odd component;   means for shifting the phase of said even component by 90 degrees and summing it with said odd component to reconstruct the non-transmitted imaginary part of said truncated summation of partial wave functions; and   means for shifting the phase of said odd component by 90 degrees and summing it with said even component to reproduce the real part of said truncated summation of partial wave functions; and   wherein said means for producing a partial wave spectrum operates on said resulting real and imaginary parts.   
     
     
       5. The apparatus as claimed in claim 3, wherein: said means for transmitting includes means for producing a continuous series of wave packets, each said packet containing a summation of partial wave functions produced by said means for truncating and having a period of a predetermined length of time, said period defining a bounded frame time;   said system input signal represents a binary bit sequence in one frame time, where said frame time further defines the period of the truncation interval; and   said system further comprises means for eliminating any discontinuities that exist at the frame boundaries including means for multiplying the truncated summation of partial wave function by an envelope function which is zero-valued at the frame boundaries.   
     
     
       6. The apparatus claimed in claim 2, wherein: said transmitted truncated summation of partial wave functions experiences inherent electronic dispersion effects in said signal channel of said system, thereby producing a frequency-dependent phase shift factor; and wherein   said system further includes means for eliminating any such dispersion of the wave functions, comprising:   means for dividing said transmitted truncated summation of partial wave functions into even and odd components;   means for shifting the phase of said even component by 90 degrees and summing it with said odd component to produce an imaginary part; and   means for shifting the phase of said odd component by 90 degrees and summing it with said even component to produce a real part; and wherein   said means for producing a partial wave spectrum operates on said resulting real and imaginary parts.   
     
     
       7. The signal processing system as claimed in claim 1, wherein: said information signal is a high resolution analog signal;   said means for truncating includes means for producing a time dependent waveform representing a truncated Z-transformation of said input signal, the truncated Z-transformed signal defining a finite sum of a series of non-orthogonal linearly independent partial wave functions; and said apparatus includes:   means for generating an interpolated clock from said time dependent waveform;   means for synchronously sampling said truncated Z-transform signal under control of said interpolated clock;   said means for detecting includes means for reconstructing said time dependent waveform to forma series of orthogonal linearly independent periodic functions;   said means for producing a partial wave spectrum includes means for producing a signal representing an inverse Z-transform of said sampled truncated Z-transform signal; and   said means for deconvolving includes means for deconvolving the inverse Z-transform signal function to reproduce said high resolution analog signal.   
     
     
       8. A method for recovering relatively high-resolution information from a partial wave representation of an information signal, comprising the steps of: producing a partial wave representation of said information signal;   synchronously selecting portions of said partial wave representation of said information signal;   producing an inverse partial wave representation of the selected portions of the transformed signal; and   linearly deconvolving said inverse partial wave representation to produce a high resolution equivalent of said information signal.   
     
     
       9. The method as claimed in claim 8, wherein: said partial wave representation is a bounded Z-transformation representation of an information signal;   said partial wave producing step includes producing a bounded Z-transformation representation of said information signal;   said synchronously selecting step includes synchronously selecting portions of the transformed signal;   said inverse partial wave producing step includes producing a signal representing an inverse Z-transform of the selected portions of the transformed signal; and   said deconvolving step includes linearly deconvolving said inverse transform signal to produce a high resolution equivalent of said information.   
     
     
       10. The method as claimed in claim 8, wherein: said partial wave producing step includes producing a truncated Z-transformation of a high resolution information signal;   said synchronously selecting step includes synchronously selecting portions of the truncated transformed signal;   said inverse partial wave producing step includes producing a signal representing an inverse Z-transform of the truncated transformed signal; and   said deconvolving step includes linearly deconvolving said inverse Z-transform signal to reconstruct the original high resolution information signal.   
     
     
       11. In a signal processing system having a system input, a signal transmission channel, and a system output, an improved method for recovering a high resolution signal at the system output corresponding to a high-resolution information signal at the system input, said method comprising the steps of: producing a summation of wave functions representing said input signal;   truncating said summation of wave functions to produce a corresponding summation of partial wave functions;   transmitting the truncated summation of partial wave functions through the signal transmission channel;   detecting the transmitted truncated summation of partial wave functions;   producing a partial wave spectrum from the detected summation of partial wave functions; and   deconvolving said partial-wave spectrum to the values of said system input signal.   
     
     
       12. The method as claimed in claim 11, wherein; said truncated summation of partial wave functions comprises real and imaginary parts; and   only said real part is transmitted through the signal transmission channel of said system.   
     
     
       13. The method as claimed in claim 11, wherein said summation of wave functions representing said input signal exists over a first interval, and said truncated summation of partial wave functions exists over a second interval, said second interval being M times shorter than said first interval, where M is the data compression ratio of the system. 
     
     
       14. The method as claimed in claim 12, wherein said real part of said transmitted signal has even and odd components, and wherein said detecting step comprises: detecting and outputting said even component;   detecting and outputting said odd component;   shifting the phase of said even component by 90 degrees and summing it with said odd component to reconstruct the non-transmitted imaginary part of said truncated summation of partial wave functions; and   shifting the phase of said odd component by 90 degrees and summing it with said even component to reproduce the real part of said truncated summation of partial wave functions; and   wherein said step of producing a partial wave spectrum utilizes said resulting real and imaginary parts.   
     
     
       15. The method as claimed in claim 13, wherein: said step of transmitting includes the step of producing a continuous series of wave packets, each said packet containing a summation of partial wave functions produced in said truncating step and having a period of a predetermined length of time, said period defining a bounded frame time;   said system input signal represents a binary bit sequence in one frame time, where said frame time further defines the period of the truncation interval; and   said method further comprises the step of eliminating any discontinuities that exist at the frame boundaries by multiplying the truncated summation of partial wave functions by an envelope function which is zero-valued at the frame boundaries.   
     
     
       16. The method claimed in claim 12, wherein: said transmitted truncated summation of partial wave functions experiences inherent electronic dispersion effects in said signal channel of said system, thereby producing a frequency-dependent phase shift factor; and wherein   said method eliminates any such dispersion of the wave functions by the steps of:   dividing said transmitted truncated summation of partial wave functions into even and odd components;   shifting the phase of said even component by 90 degrees and summing it with said odd component to produce an imaginary part; and   shifting the phase of said odd component by 90 degrees and summing it with said even component to produce a real part; and wherein   said step of producing a partial wave spectrum utilizes said resulting real and imaginary parts.   
     
     
       17. The method as claimed in claim 11, wherein: said information signal is a high resolution analog signal;   said step of producing a summation of wave functions includes producing a time dependent waveform representing a truncated Z-transformation of said input signal, the truncated Z-transformed signal defining a finite sum of a series of non-orthogonal linearly independent partial wave functions; and said method includes the steps of:   generating an interpolated clock from said time dependent waveform;   synchronously sampling said truncated Z-transformed signal under control of said interpolated clock; and   said detecting step includes reconstructing said time dependent waveform to form a series of orthogonal linearly independent periodic functions;   said partial wave spectrum producing step includes producing a signal representing an inverse Z-transform of said sampled truncated Z-transformed signal; and   said deconvolving step includes deconvolving the inverse transform signal to reproduce said high resolution analog signal.   
     
     
       18. The method as claimed in claim 17, for use in a signal processing system having digital circuit components and a system clock operating at a prescribed frequency, said method recovering relatively high-resolution information contained in a bounded Z-transformation representation of a high resolution information signal; said step of producing a summation of wave functions includes producing a bounded Z-transformation representation of said information signal;   said detecting step includes synchronously selecting portions of the transformed signal at a frequency M times the frequency of said system clock;   said partial wave spectrum producing step includes producing a signal representing an inverse Z-transform of the selected portions of the Z-transformed signal; and   said deconvolving step includes linearly deconvolving said inverse Z-transform signal to reproduce a high resolution equivalent of said information signal.   
     
     
       19. An information transreceive system having a signal transmission channel, comprising: a partial wave generator for receiving a relatively high resolution information input signal and generating a partial wave representation of said input signal for transmission through said transmission channel;   an analytic signal converter for receiving the partial wave representation from said transmission channel and removing the effects of dispersion of the transmitted signal in said transmission channel;   a partial wave detector for converting the dispersion free signal from said analytic converter to a relatively low resolution spectrum as compared to said input signal; and   a linear deconvolver for reconstructing a relatively high resolution signal from said relatively low resolution spectrum.   
     
     
       20. The system as claimed in claim 19, wherein said linear deconvolver includes: a deconvolution matrix;   means for selective multiplication of said relatively low resolution spectrum with said deconvolution matrix; and   a zero crossing detector responsive to said selective multiplication means to thereby produce said relatively high resolution signal.   
     
     
       21. The system as claimed in claim 19, comprising a clock generator and data synchronizer at the transmitting and of said transmission channel for generating a relatively high speed clock and a relatively low speed sync signal, and wherein:   said partial wave generator includes means for sampling said partial wave representation of said input signal under control of said high speed clock;   said clock generator and data synchronizer including a divide-by-M circuit receiving said high speed clock and outputting a relatively low speed channel clock having a frequency 1/M times said high speed clock;   said partial wave generator including a summing circuit for summing said partial wave representation and said low speed channel clock to thereby produce a composite signal having a low frequency channel clock component for transmission through said transmission channel; and   said partial wave generator is synchronously operated under control of said relatively low speed sync signal.   
     
     
       22. The system as claimed in claim 21, wherein said partial wave generator includes means responsive to said low speed sync signal to produce a continuous stream of partial wave packets, each wave packet being created during the time frame of a period of said low speed sync signal, thereby defining frame boundaries and a frame rate equal to the frequency of said low speed sync signal.   
     
     
       23. The system as claim in claim 21, wherein said clock generator and synchronizer includes means for coupling said low speed sync signal to said high speed clock for temporarily shifting the frequency of said high speed clock for a brief time period at said low speed sync signal rate, thereby introducing a low speed sync signal component into said composite signal being transmitted through said transmission channel.   
     
     
       24. The system as claimed in claim 23, comprising a clock detector, interpolator, and frame synchronizer at the receiving end of said transmission channel, including   means for extracting said low frequency channel clock component from said transmitted composite signal;   means for generating a high speed receiver clock;   means for extracting said sync signal component from said transmitted composite signal;   means for synchronizing said high speed receiver clock with said extracted sync signal and extracted low frequency channel clock to set the frequency of said high speed receiver clock at M times the frequency of the extracted channel clock; and   wherein said partial wave detector includes means for desampling said transmitted composite signal under control of and at the frequency of said high frequency receiver clock.   
     
     
       25. The system as claimed in claim 24, wherein said partial wave generator includes means responsive to said low speed sync signal to produce a continuous stream of partial wave packets, each wave packet being created during the time frame of a period of said low speed sync signal, thereby defining frame boundaries and a frame rate equal to the frequency of said low speed sync signal, and wherein said system further includes means for coupling said extracted sync signal to said partial wave detector for identifying frame times for synchronous operation of said partial wave detector.   
     
     
       26. The system as claimed in claim 24, wherein: said high speed receiver clock generating means includes a voltage controlled oscillator, and a stable high frequency reference oscillator, said voltage controlled oscillator oscillating at said reference frequency;   said clock detector, interpolator and frame synchronizer includes a divide-by-M circuit for dividing the output of said voltage controlled oscillator by M;   said receiver clock generator includes a frequency comparator for comparing said extracted low frequency channel clock with said voltage controlled oscillator output divided by M, and producing a voltage proportional to the frequency difference for application to said voltage controlled oscillator for altering the frequency of said voltage controlled oscillator in such a direction to reduce said frequency difference to zero.   
     
     
       27. The system as claimed in claim 26, wherein said frequency comparator develops a pulse at its output when said extracted low frequency channel clock frequency is shifted discontinuously at sync signal times. 
     
     
       28. The system as claimed in claim 22, wherein said partial wave generator comprises: a Z-transformer receiving said high resolution input signal and performing a Z-transform thereon;   a window function generator; and   a multiplier for multiplying the output of the Z-transformer with said window function.   
     
     
       29. The system as claimed in claim 28, wherein: said window function generator is adapted to produce a Gaussian function whose value is substantially zero at said frame boundaries.   
     
     
       30. The system as claimed in claim 19, wherein: said partial wave detector comprises an inverse Z-transformer. 
     
     
       31. Apparatus for recovering relatively high-resolution information from a partial wave representation of an information signal, comprising: means for producing a partial wave representation of said information signal;   means for synchronously selecting portions of said partial wave representation of said information signal;   means for producing an inverse partial wave representation of the selected portions of the transformed signal; and   means for linearly deconvolving said inverse partial wave representation to produce a high resolution equivalent of said information signal.   
     
     
       32. The apparatus as claimed in claim 31 for use in a system timed by a system clock of a prescribed frequency, wherein: said means for synchronously selecting portions of said partial wave representation comprises waveform sampling circuitry; and   said apparatus further comprises means for producing an interpolated clock at a frequency M times the frequency of said system clock, said interpolated clock defining the sampling rate of said sampling circuit.   
     
     
       33. The apparatus as claimed in claim 31, wherein: said system is a transreceive system comprising a transmitting apparatus and a receiving apparatus for transmitting and receiving information over an information transmission channel;   said means for synchronously selecting portions of said partial wave representation comprises a waveform sampling means in said transmitting apparatus and a waveform desampling means in said receiving apparatus; and   said interpolated clock producing means resides in said receiving apparatus for application to said desampling means as a desampling clock.   
     
     
       34. The apparatus as claimed in claim 32, wherein: said system is an analyzer system comprising an optomechanical source of partial wave function;   said optomechanical source includes a laser device for producing a laser beam, and a sensor therefor for producing a laser fringe clock as a result of altering the path of said laser beam, said laser fringe clock defining said system clock; and   said means for producing an interpolated clock includes means for correlating a high speed clock with a means for altering said path of said laser beam in a controlled manner.   
     
     
       35. A signal analyzer system, comprising: a partial wave generator for generating a partial wave representation of a relatively high resolution information signal;   a clock generator for producing a relatively low frequency first clock and a relatively high frequency second clock;   means for synchronously selecting portions of said partial wave representation;   a partial wave detector for converting the synchronously selected portions to a relatively low resolution spectrum; and   a linear deconvolver for reconstructing the relatively high resolution information signal from said rlatively low resolution spectrum; means for coupling said first clock to said partial wave generator as a timing reference; and   means for coupling said second clock to said means for synchronously selecting as a timing reference.   
     
     
       36. The system as claimed in claim 35, wherein the ratio of the frequency of said second clock to the frequency of said first clock defines a data compression ratio M for said system. 
     
     
       37. The system as claimed in claim 36, wherein: said partial wave generator comprises means for producing a dispersed truncated interferogram including a light beam source and a means for effecting variable phase retardation of said light beam; and   M equals the ratio of the extent of phase retardation for a full spectrum interferogram to that of said truncated interferogram.   
     
     
       38. The system as claimed in claim 35, where said means for synchronously selecting portions of said partial wave representation comprises a data sampling circuit. 
     
     
       39. The system as claimed in claim 37, wherein: said partial wave detector comprises an analytic converter for receiving the partial wave representation from said partial wave generator, and for removing the effects of dispersion of the dispersed truncated interferogram, said partial wave detector converting the dispersion free truncated interferogram to said relatively low resolution spectrum.   
     
     
       40. The system as claimed in claim 39, wherein: said partial wave detector further including an inverse Z-transformer intercoupled between said analytic converter and said linear deconvolver.   
     
     
       41. The system as claimed in claim 35, wherein said linear deconvolver includes: a deconvolution matrix;   means for selective multiplication of said relatively low resolution spectrum with said deconvolution matrix; and   a zero crossing detector responsive to said selective multiplication means to thereby produce said relatively high resolution information signal.   
     
     
       42. The system as claimed in claim 35, wherein: said means for synchronously selecting includes means for sampling said partial wave representation of said high resolution information signal under control of said high frequency clock;   said clock generator including a divide-by-M circuit receiving said high frequency clock and outputting said relatively low frequency clock having a frequency 1/M times said high frequency clock.   
     
     
       43. The system as claimed in claim 37, wherein: said high frequency clock generating means includes a stable high frequency reference oscillator;   said clock generator includes:   a laser and laser beam detector, said laser beam being subjected to said variable phase retardation to product a laser fringe clock at the output of said laser beam detector;   a divide-by-M circuit for dividing the output of said high frequency reference oscillator; and   a frequency comparator for comparing said laser fringe clock frequency with said high frequency reference oscillator output divided by M, and producing a voltage proportional to the frequency difference for application to said interferometer producing means for varying the rate of phase retardation in such a direction to reduce said frequency difference to zero.   
     
     
       44. The system as claimed in claim 35, wherein said partial wave generator comprises: a Z-transformer generating device capable of producing said representation of a high resolution information signal;   a window function generator; and   a multiplier for multiplying the output of the Z-transformer with said window function.   
     
     
       45. The system as claimed in claim 44, wherein: said system comprises an interferometer having movable phase retardation means defining said Z-transformer generating device; and   said window function is generated by a limited movement of said movable phase retardation means.   
     
     
       46. The system as claimed in claim 28, wherein: said window function generator is adapted to produce a Gaussian function whose value is substantially zero at the extremes of said window function.   
     
     
       47. The system as claimed in claim 35 timed by low frequency clock of a prescribed frequency, wherein: said means for synchronously selecting portions of said partial wave representation comprises waveform sampling circuitry; and   said system further comprises means for producing an interpolated clock at a frequency M times the frequency of said low frequency clock, said interpolated clock defining the sampling rate of said sampling circuit.   
     
     
       48. The system as claimed in claim 35, wherein: said partial wave detector includes an inverse Z-transformer for producing said relatively low resolution spectrum.   
     
     
       49. The system as claimed in claim 35, wherein said Z-transformer is a chirp Z-transformer.